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Diffusion-driven instability and bifurcation in the Lengyel-Epstein system. (English) Zbl 1146.35384

Summary: Lengyel-Epstein reaction-diffusion system of the CIMA reaction is considered. We derive the precise conditions on the parameters so that the spatial homogeneous equilibrium solution and the spatial homogeneous periodic solution become Turing unstable or diffusively unstable. We also perform a detailed Hopf bifurcation analysis to both the ODE and PDE models, and derive conditions for determining the bifurcation direction and the stability of the bifurcating periodic solution.

MSC:

35K57 Reaction-diffusion equations
35B10 Periodic solutions to PDEs
35K50 Systems of parabolic equations, boundary value problems (MSC2000)
92B05 General biology and biomathematics
35B32 Bifurcations in context of PDEs
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